Journal of Scientific Computing

, Volume 78, Issue 3, pp 1942–1961 | Cite as

A Contour-Integral Based Method for Counting the Eigenvalues Inside a Region

  • Guojian YinEmail author


In many applications, the information about the number of eigenvalues inside a given region is required. In this work, we develop a contour-integral based method for this purpose. Our method is motivated by two findings. There exist methods for estimating the number of eigenvalues inside a region in the complex plane, but our method is able to compute the number exactly. Our method has a good potential to be implemented on a high-performance parallel architecture. Numerical experiments are reported to show the viability of our method.


Eigenvalue Generalized eigenvalue problem Contour integral Spectral projection 

Mathematics Subject Classification

15A18 58C40 65F15 



I would like to thank Professor Raymond H. Chan, my thesis advisor, for his help in preparing this paper. I also would like to thank the anonymous reviewers for their useful suggestions which have greatly improved this paper. This work was supported by the National Natural Science Foundation of China (NSFC) under Grant 11701593.


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Authors and Affiliations

  1. 1.School of MathematicsSun Yat-sen UniversityGuangzhouPeople’s Republic of China

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